1/* LibTomMath, multiple-precision integer library -- Tom St Denis 2 * 3 * LibTomMath is a library that provides multiple-precision 4 * integer arithmetic as well as number theoretic functionality. 5 * 6 * The library was designed directly after the MPI library by 7 * Michael Fromberger but has been written from scratch with 8 * additional optimizations in place. 9 * 10 * The library is free for all purposes without any express 11 * guarantee it works. 12 * 13 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com 14 */ 15#ifndef BN_H_ 16#define BN_H_ 17 18#include <stdio.h> 19#include <string.h> 20#include <stdlib.h> 21#include <ctype.h> 22#include <limits.h> 23 24#include <tommath_class.h> 25 26#ifndef MIN 27 #define MIN(x,y) ((x)<(y)?(x):(y)) 28#endif 29 30#ifndef MAX 31 #define MAX(x,y) ((x)>(y)?(x):(y)) 32#endif 33 34#ifdef __cplusplus 35extern "C" { 36 37/* C++ compilers don't like assigning void * to mp_digit * */ 38#define OPT_CAST(x) (x *) 39 40#else 41 42/* C on the other hand doesn't care */ 43#define OPT_CAST(x) 44 45#endif 46 47 48/* detect 64-bit mode if possible */ 49#if defined(__x86_64__) 50 #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) 51 #define MP_64BIT 52 #endif 53#endif 54 55/* some default configurations. 56 * 57 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits 58 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits 59 * 60 * At the very least a mp_digit must be able to hold 7 bits 61 * [any size beyond that is ok provided it doesn't overflow the data type] 62 */ 63#ifdef MP_8BIT 64 typedef unsigned char mp_digit; 65 typedef unsigned short mp_word; 66#elif defined(MP_16BIT) 67 typedef unsigned short mp_digit; 68 typedef unsigned long mp_word; 69#elif defined(MP_64BIT) 70 /* for GCC only on supported platforms */ 71#ifndef CRYPT 72 typedef unsigned long long ulong64; 73 typedef signed long long long64; 74#endif 75 76 typedef unsigned long mp_digit; 77 typedef unsigned long mp_word __attribute__ ((mode(TI))); 78 79 #define DIGIT_BIT 60 80#else 81 /* this is the default case, 28-bit digits */ 82 83 /* this is to make porting into LibTomCrypt easier :-) */ 84#ifndef CRYPT 85 #if defined(_MSC_VER) || defined(__BORLANDC__) 86 typedef unsigned __int64 ulong64; 87 typedef signed __int64 long64; 88 #else 89 typedef unsigned long long ulong64; 90 typedef signed long long long64; 91 #endif 92#endif 93 94 typedef unsigned long mp_digit; 95 typedef ulong64 mp_word; 96 97#ifdef MP_31BIT 98 /* this is an extension that uses 31-bit digits */ 99 #define DIGIT_BIT 31 100#else 101 /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ 102 #define DIGIT_BIT 28 103 #define MP_28BIT 104#endif 105#endif 106 107/* define heap macros */ 108#ifndef CRYPT 109 /* default to libc stuff */ 110 #ifndef XMALLOC 111 #define XMALLOC malloc 112 #define XFREE free 113 #define XREALLOC realloc 114 #define XCALLOC calloc 115 #else 116 /* prototypes for our heap functions */ 117 extern void *XMALLOC(size_t n); 118 extern void *XREALLOC(void *p, size_t n); 119 extern void *XCALLOC(size_t n, size_t s); 120 extern void XFREE(void *p); 121 #endif 122#endif 123 124 125/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ 126#ifndef DIGIT_BIT 127 #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */ 128#endif 129 130#define MP_DIGIT_BIT DIGIT_BIT 131#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) 132#define MP_DIGIT_MAX MP_MASK 133 134/* equalities */ 135#define MP_LT -1 /* less than */ 136#define MP_EQ 0 /* equal to */ 137#define MP_GT 1 /* greater than */ 138 139#define MP_ZPOS 0 /* positive integer */ 140#define MP_NEG 1 /* negative */ 141 142#define MP_OKAY 0 /* ok result */ 143#define MP_MEM -2 /* out of mem */ 144#define MP_VAL -3 /* invalid input */ 145#define MP_RANGE MP_VAL 146 147#define MP_YES 1 /* yes response */ 148#define MP_NO 0 /* no response */ 149 150/* Primality generation flags */ 151#define LTM_PRIME_BBS 0x0001 /* BBS style prime */ 152#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ 153#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ 154 155typedef int mp_err; 156 157/* you'll have to tune these... */ 158extern int KARATSUBA_MUL_CUTOFF, 159 KARATSUBA_SQR_CUTOFF, 160 TOOM_MUL_CUTOFF, 161 TOOM_SQR_CUTOFF; 162 163/* define this to use lower memory usage routines (exptmods mostly) */ 164/* #define MP_LOW_MEM */ 165 166/* default precision */ 167#ifndef MP_PREC 168 #ifndef MP_LOW_MEM 169 #define MP_PREC 32 /* default digits of precision */ 170 #else 171 #define MP_PREC 8 /* default digits of precision */ 172 #endif 173#endif 174 175/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ 176#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) 177 178/* the infamous mp_int structure */ 179typedef struct { 180 int used, alloc, sign; 181 mp_digit *dp; 182} mp_int; 183 184/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ 185typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); 186 187 188#define USED(m) ((m)->used) 189#define DIGIT(m,k) ((m)->dp[(k)]) 190#define SIGN(m) ((m)->sign) 191 192/* error code to char* string */ 193char *mp_error_to_string(int code); 194 195/* ---> init and deinit bignum functions <--- */ 196/* init a bignum */ 197int mp_init(mp_int *a); 198 199/* free a bignum */ 200void mp_clear(mp_int *a); 201 202/* init a null terminated series of arguments */ 203int mp_init_multi(mp_int *mp, ...); 204 205/* clear a null terminated series of arguments */ 206void mp_clear_multi(mp_int *mp, ...); 207 208/* exchange two ints */ 209void mp_exch(mp_int *a, mp_int *b); 210 211/* shrink ram required for a bignum */ 212int mp_shrink(mp_int *a); 213 214/* grow an int to a given size */ 215int mp_grow(mp_int *a, int size); 216 217/* init to a given number of digits */ 218int mp_init_size(mp_int *a, int size); 219 220/* ---> Basic Manipulations <--- */ 221#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) 222#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) 223#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) 224#define mp_isneg(a) (((a)->sign) ? MP_YES : MP_NO) 225 226/* set to zero */ 227void mp_zero(mp_int *a); 228 229/* set to zero, multi */ 230void mp_zero_multi(mp_int *a, ...); 231 232/* set to a digit */ 233void mp_set(mp_int *a, mp_digit b); 234 235/* set a 32-bit const */ 236int mp_set_int(mp_int *a, unsigned long b); 237 238/* get a 32-bit value */ 239unsigned long mp_get_int(mp_int * a); 240 241/* initialize and set a digit */ 242int mp_init_set (mp_int * a, mp_digit b); 243 244/* initialize and set 32-bit value */ 245int mp_init_set_int (mp_int * a, unsigned long b); 246 247/* copy, b = a */ 248int mp_copy(mp_int *a, mp_int *b); 249 250/* inits and copies, a = b */ 251int mp_init_copy(mp_int *a, mp_int *b); 252 253/* trim unused digits */ 254void mp_clamp(mp_int *a); 255 256/* ---> digit manipulation <--- */ 257 258/* right shift by "b" digits */ 259void mp_rshd(mp_int *a, int b); 260 261/* left shift by "b" digits */ 262int mp_lshd(mp_int *a, int b); 263 264/* c = a / 2**b */ 265int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); 266 267/* b = a/2 */ 268int mp_div_2(mp_int *a, mp_int *b); 269 270/* c = a * 2**b */ 271int mp_mul_2d(mp_int *a, int b, mp_int *c); 272 273/* b = a*2 */ 274int mp_mul_2(mp_int *a, mp_int *b); 275 276/* c = a mod 2**d */ 277int mp_mod_2d(mp_int *a, int b, mp_int *c); 278 279/* computes a = 2**b */ 280int mp_2expt(mp_int *a, int b); 281 282/* Counts the number of lsbs which are zero before the first zero bit */ 283int mp_cnt_lsb(mp_int *a); 284 285/* I Love Earth! */ 286 287/* makes a pseudo-random int of a given size */ 288int mp_rand(mp_int *a, int digits); 289 290/* ---> binary operations <--- */ 291/* c = a XOR b */ 292int mp_xor(mp_int *a, mp_int *b, mp_int *c); 293 294/* c = a OR b */ 295int mp_or(mp_int *a, mp_int *b, mp_int *c); 296 297/* c = a AND b */ 298int mp_and(mp_int *a, mp_int *b, mp_int *c); 299 300/* ---> Basic arithmetic <--- */ 301 302/* b = -a */ 303int mp_neg(mp_int *a, mp_int *b); 304 305/* b = |a| */ 306int mp_abs(mp_int *a, mp_int *b); 307 308/* compare a to b */ 309int mp_cmp(mp_int *a, mp_int *b); 310 311/* compare |a| to |b| */ 312int mp_cmp_mag(mp_int *a, mp_int *b); 313 314/* c = a + b */ 315int mp_add(mp_int *a, mp_int *b, mp_int *c); 316 317/* c = a - b */ 318int mp_sub(mp_int *a, mp_int *b, mp_int *c); 319 320/* c = a * b */ 321int mp_mul(mp_int *a, mp_int *b, mp_int *c); 322 323/* b = a*a */ 324int mp_sqr(mp_int *a, mp_int *b); 325 326/* a/b => cb + d == a */ 327int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 328 329/* c = a mod b, 0 <= c < b */ 330int mp_mod(mp_int *a, mp_int *b, mp_int *c); 331 332/* ---> single digit functions <--- */ 333 334/* compare against a single digit */ 335int mp_cmp_d(mp_int *a, mp_digit b); 336 337/* c = a + b */ 338int mp_add_d(mp_int *a, mp_digit b, mp_int *c); 339 340/* c = a - b */ 341int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); 342 343/* c = a * b */ 344int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); 345 346/* a/b => cb + d == a */ 347int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); 348 349/* a/3 => 3c + d == a */ 350int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); 351 352/* c = a**b */ 353int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); 354 355/* c = a mod b, 0 <= c < b */ 356int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); 357 358/* ---> number theory <--- */ 359 360/* d = a + b (mod c) */ 361int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 362 363/* d = a - b (mod c) */ 364int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 365 366/* d = a * b (mod c) */ 367int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 368 369/* c = a * a (mod b) */ 370int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); 371 372/* c = 1/a (mod b) */ 373int mp_invmod(mp_int *a, mp_int *b, mp_int *c); 374 375/* c = (a, b) */ 376int mp_gcd(mp_int *a, mp_int *b, mp_int *c); 377 378/* produces value such that U1*a + U2*b = U3 */ 379int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); 380 381/* c = [a, b] or (a*b)/(a, b) */ 382int mp_lcm(mp_int *a, mp_int *b, mp_int *c); 383 384/* finds one of the b'th root of a, such that |c|**b <= |a| 385 * 386 * returns error if a < 0 and b is even 387 */ 388int mp_n_root(mp_int *a, mp_digit b, mp_int *c); 389 390/* special sqrt algo */ 391int mp_sqrt(mp_int *arg, mp_int *ret); 392 393/* is number a square? */ 394int mp_is_square(mp_int *arg, int *ret); 395 396/* computes the jacobi c = (a | n) (or Legendre if b is prime) */ 397int mp_jacobi(mp_int *a, mp_int *n, int *c); 398 399/* used to setup the Barrett reduction for a given modulus b */ 400int mp_reduce_setup(mp_int *a, mp_int *b); 401 402/* Barrett Reduction, computes a (mod b) with a precomputed value c 403 * 404 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely 405 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. 406 */ 407int mp_reduce(mp_int *a, mp_int *b, mp_int *c); 408 409/* setups the montgomery reduction */ 410int mp_montgomery_setup(mp_int *a, mp_digit *mp); 411 412/* computes a = B**n mod b without division or multiplication useful for 413 * normalizing numbers in a Montgomery system. 414 */ 415int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); 416 417/* computes x/R == x (mod N) via Montgomery Reduction */ 418int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 419 420/* returns 1 if a is a valid DR modulus */ 421int mp_dr_is_modulus(mp_int *a); 422 423/* sets the value of "d" required for mp_dr_reduce */ 424void mp_dr_setup(mp_int *a, mp_digit *d); 425 426/* reduces a modulo b using the Diminished Radix method */ 427int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); 428 429/* returns true if a can be reduced with mp_reduce_2k */ 430int mp_reduce_is_2k(mp_int *a); 431 432/* determines k value for 2k reduction */ 433int mp_reduce_2k_setup(mp_int *a, mp_digit *d); 434 435/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ 436int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); 437 438/* returns true if a can be reduced with mp_reduce_2k_l */ 439int mp_reduce_is_2k_l(mp_int *a); 440 441/* determines k value for 2k reduction */ 442int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); 443 444/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ 445int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); 446 447/* d = a**b (mod c) */ 448int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 449 450/* ---> Primes <--- */ 451 452/* number of primes */ 453#ifdef MP_8BIT 454 #define PRIME_SIZE 31 455#else 456 #define PRIME_SIZE 256 457#endif 458 459/* table of first PRIME_SIZE primes */ 460extern const mp_digit ltm_prime_tab[]; 461 462/* result=1 if a is divisible by one of the first PRIME_SIZE primes */ 463int mp_prime_is_divisible(mp_int *a, int *result); 464 465/* performs one Fermat test of "a" using base "b". 466 * Sets result to 0 if composite or 1 if probable prime 467 */ 468int mp_prime_fermat(mp_int *a, mp_int *b, int *result); 469 470/* performs one Miller-Rabin test of "a" using base "b". 471 * Sets result to 0 if composite or 1 if probable prime 472 */ 473int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result); 474 475/* This gives [for a given bit size] the number of trials required 476 * such that Miller-Rabin gives a prob of failure lower than 2^-96 477 */ 478int mp_prime_rabin_miller_trials(int size); 479 480/* performs t rounds of Miller-Rabin on "a" using the first 481 * t prime bases. Also performs an initial sieve of trial 482 * division. Determines if "a" is prime with probability 483 * of error no more than (1/4)**t. 484 * 485 * Sets result to 1 if probably prime, 0 otherwise 486 */ 487int mp_prime_is_prime(mp_int *a, int t, int *result); 488 489/* finds the next prime after the number "a" using "t" trials 490 * of Miller-Rabin. 491 * 492 * bbs_style = 1 means the prime must be congruent to 3 mod 4 493 */ 494int mp_prime_next_prime(mp_int *a, int t, int bbs_style); 495 496/* makes a truly random prime of a given size (bytes), 497 * call with bbs = 1 if you want it to be congruent to 3 mod 4 498 * 499 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can 500 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself 501 * so it can be NULL 502 * 503 * The prime generated will be larger than 2^(8*size). 504 */ 505#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat) 506 507/* makes a truly random prime of a given size (bits), 508 * 509 * Flags are as follows: 510 * 511 * LTM_PRIME_BBS - make prime congruent to 3 mod 4 512 * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) 513 * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero 514 * LTM_PRIME_2MSB_ON - make the 2nd highest bit one 515 * 516 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can 517 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself 518 * so it can be NULL 519 * 520 */ 521int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); 522 523int mp_find_prime(mp_int *a); 524 525int mp_isprime(mp_int *a); 526 527/* ---> radix conversion <--- */ 528int mp_count_bits(mp_int *a); 529 530int mp_unsigned_bin_size(mp_int *a); 531int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); 532int mp_to_unsigned_bin(mp_int *a, unsigned char *b); 533int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 534 535int mp_signed_bin_size(mp_int *a); 536int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); 537int mp_to_signed_bin(mp_int *a, unsigned char *b); 538int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 539 540int mp_read_radix(mp_int *a, const char *str, int radix); 541int mp_toradix(mp_int *a, char *str, int radix); 542int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); 543int mp_radix_size(mp_int *a, int radix, int *size); 544 545int mp_fread(mp_int *a, int radix, FILE *stream); 546int mp_fwrite(mp_int *a, int radix, FILE *stream); 547 548#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) 549#define mp_raw_size(mp) mp_signed_bin_size(mp) 550#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) 551#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) 552#define mp_mag_size(mp) mp_unsigned_bin_size(mp) 553#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) 554 555#define mp_tobinary(M, S) mp_toradix((M), (S), 2) 556#define mp_tooctal(M, S) mp_toradix((M), (S), 8) 557#define mp_todecimal(M, S) mp_toradix((M), (S), 10) 558#define mp_tohex(M, S) mp_toradix((M), (S), 16) 559 560/* lowlevel functions, do not call! */ 561int s_mp_add(mp_int *a, mp_int *b, mp_int *c); 562int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); 563#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) 564int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 565int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 566int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 567int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 568int fast_s_mp_sqr(mp_int *a, mp_int *b); 569int s_mp_sqr(mp_int *a, mp_int *b); 570int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); 571int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); 572int mp_karatsuba_sqr(mp_int *a, mp_int *b); 573int mp_toom_sqr(mp_int *a, mp_int *b); 574int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); 575int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); 576int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 577int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); 578int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); 579void bn_reverse(unsigned char *s, int len); 580 581extern const char *mp_s_rmap; 582 583#ifdef __cplusplus 584 } 585#endif 586 587#endif 588 589 590/* $Source: /cvs/libtom/libtommath/tommath.h,v $ */ 591/* $Revision: 1.8 $ */ 592/* $Date: 2006/03/31 14:18:44 $ */ 593